• How To Reinstall MacOS From MacOS Recovery - Apple Support
• How To Reformat A Used Mac - Apple Community

First, don't reformat. That's a windows thing. But if you must...

power off, hold down command + r power on. Puts you in recovery mode.

Aug 10, 2020 macOS Recovery makes it easy to reinstall the Mac operating system, even if you need to erase your startup disk first. All you need is a connection to the Internet. If a wireless network is available, you can choose it from the Wi-Fi menu, which is also available in macOS Recovery. Feb 24, 2017 Factory Reset MacBook Pro and other Macs Using MacOS Recovery. Once you have done with all the above tasks, you can factory reset your MacBook Pro or any other Mac’s using MacOS Recovery tool. Note: Follow this reset process is only if you are keeping your MacBook. If you are selling or giving away your MacBook, then follow the next method. Have you have erased the start-up disk? Then it is time for you to consider formatting your MacBook Pro. Here are the steps to guide you through formatting a MacBook Pro. Erasing MacBook Drive and installing a clean version of OS X 1. Turn on your MacBook Pro Firstly, you need to turn on your MacBook Pro and wait until you hear the start-up sound. Whether you want to factory reset MacBook Pro or reinstall macOS, make sure your Mac is under a good internet connection. Restore MacBook Pro to factory settings. Step 1 Click on 'Apple Menu' on the top bar and choose 'Restart' option. Step 2 When your MacBook Pro reboots, press 'Commend' and 'R' at the same time when you hear the Apple startup.

Figure out what the problems is.

Look into running activity monitor.

How To Reinstall MacOS From MacOS Recovery - Apple Support

Some semi-random thoughts on addressing performance problems.

Activity Monitor
Look at what is happening with your Mac when you run Activity Monitor.

Macintosh-HD -> Applications -> Utilities -> Activity Monitor

Look at my activity monitor image below.

You want to monitor the cpu time:

make certain:

1) little arrow appears in the %CPU column

2) little arrow is in the down direction

3) Activity Monitor is monitoring (All Processes)

4( Make sure that you have clicked on the cpu tab.

Use the View menu to change to All Processes if needed.

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You can gain some understanding of Activity Monitor by looking at it every once in a while. Look at the small graph below to see the total cpu time used. See what processes are listed on top.

Here is how I have my cpu display set up for Yosemite.

AppleJack
'AppleJack is a user friendly troubleshooting assistant for Mac OS X. With AppleJack you can troubleshoot a computer even if you can't load the GUI, or don't have a startup CD handy. AppleJack runs in Single User Mode and is menu-based for ease of use.'
http://applejack.sourceforge.net/

Console
You can use the console application to examine Mac OS log files. The logs will contain information on various system processes.

Macintosh-HD -> Applications -> Utilities -> Console

File > open console log
this will display the startup messages

and
file > open system log
once the system is started, messages will go into the system log

Other folks
bdaqua advises running disk utility from install disk ( or recover partition ) and performing a safe boot:
https://discussions.apple.com/thread/2256611
Using the Recovery partition

Hold down command+r at boot.
http://support.apple.com/en-us/HT4718
http://osxdaily.com/2012/02/03/how-to-boot-into-os-x-lions-recovery-hd-partition /

How To Reformat A Used Mac - Apple Community

K Shaffer advises checking for available RAM